Worksheet: Rational and Irrational Numbers

In this worksheet, we will practice identifying and telling the difference between rational and irrational numbers.

Q1:

Is 𝜋 a rational or an irrational number?

Aan irrational number

Ba rational number

Q2:

What type of number is √32?

ARational

BInteger

CIrrational

Q3:

Is 0.4 a rational or an irrational number?

Aa rational number

Ban irrational number

Q4:

All integers are numbers.

Arational

Birrational

Q5:

I have a number that cannot be expressed in
the form 𝑎𝑏 where 𝑎, 𝑏∈ℤ
and 𝑏≠0.
Is this number rational or irrational?

Airrational number

Brational number

Q6:

Is 7 a rational or an irrational number?

Aan irrational number

Ba rational number

Q7:

Is 12 a rational or an irrational number?

Aa rational number

Ban irrational number

Q8:

According to the US Mint, the diameter of a quarter is 0.955 inches.
The circumference of the quarter would be the diameter multiplied by 𝜋.
Is the circumference of a quarter a whole number, a rational number, or an irrational number?

Arational number

Birrational number

Cwhole number

Q9:

What type of number is 12? Select all that apply.

Ainteger

Brational

Cirrational

Q10:

What type of number is √2? Select all that apply.

Airrational

Binteger

Crational

Q11:

Is √2 a rational or an irrational number?

Aa rational number

Ban irrational number

Q12:

What type of number is 𝜋? Select all that apply.

Arational

Binteger

Cirrational

Q13:

Is 𝑒 a rational or an irrational number?

Aan irrational number

Ba rational number

Q14:

Is 0.456 a rational or an irrational number?

Aan irrational number

Ba rational number

Q15:

Without using a calculator, order the numbers −4𝜋, −4√3, 𝜋,12 and −3√4 from smallest to largest.

A−4𝜋, −3√4, −4√3, 𝜋, 12

B−4𝜋, −4√3, −3√4, 𝜋, 12

C−4𝜋, −4√3, −3√4, 12, 𝜋

D12, 𝜋, −4√3, −3√4, −4𝜋

E−3√4, −4√3, 𝜋, 12, −4𝜋

Q16:

Without using a calculator, order the numbers 8, 7, and
√66 from smallest to largest.

A8,√66,7

B√66,8,7

C7,√66,8

D7,8,√66

E√66,7,8

Q17:

On the number line, which arrow represents the value of 𝜋?

Ab

Bc

Ca

Q18:

Mason wants to estimate the value of 𝜋. He knows that 𝜋 is 3.14 to two decimal places but decides to round
this to the nearest whole number to make this estimate easier to calculate.

What will his estimate of 𝜋 be?

Mason wants to check whether his approximation is accurate to the nearest whole number, so he rounds 𝜋 to 3.1.
What will his approximation of 𝜋 be now?

Hence, what is an approximation of 𝜋 accurate to the nearest whole number?

Q19:

Without using a calculator, order the numbers 𝜋, √2, 1, 2, and
√3 from smallest to largest.

A𝜋, √3, 2, √2, 1

B1, √2, 2, √3, 𝜋

C1, √2, √3, 2, 𝜋

D√2, 1, √3, 2, 𝜋

E𝜋, 2, √3, √2, 1

Q20:

If a rational number is not a perfect square, will its square root be rational or irrational?

Arational

Birrational

CIt could be either.

Q21:

What is ℚ∩ℚ′?

A∅

Bℤ

C{0}

Dℚ

Q22:

What is ℚ−ℚ′?

Aℚ

B{0}

C∅

Dℤ

Q23:

Which of the following is an irrational number that lies between 2 and 3?

A√3

B52

C2.6

D√7

E√10

Q24:

A square of side length 𝑥 cm has an area of 280 cm2. Which of the following is true about 𝑥?